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OPTIMAL TIME-CONSISTENT PORTFOLIO AND CONTRIBUTION SELECTION FOR DEFINED BENEFIT PENSION SCHEMES UNDER MEAN–VARIANCE CRITERION

Part of: Stochastic systems and control Mathematical finance Mathematical economics

Published online by Cambridge University Press:  09 October 2014

XIAOQING LIANG ,
LIHUA BAI  and
JUNYI GUO
XIAOQING LIANG
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 30007, SC, PR China email [email protected], [email protected], [email protected]
LIHUA BAI
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 30007, SC, PR China email [email protected], [email protected], [email protected]
JUNYI GUO*
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 30007, SC, PR China email [email protected], [email protected], [email protected]
*
✉[email protected]
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Abstract

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We investigate two mean–variance optimization problems for a single cohort of workers in an accumulation phase of a defined benefit pension scheme. Since the mortality intensity evolves as a general Markov diffusion process, the liability is random. The fund manager aims to cover this uncertain liability via controlling the asset allocation strategy and the contribution rate. In order to have a more realistic model, we study the case when the risk aversion depends dynamically on current wealth. By solving an extended Hamilton–Jacobi–Bellman system, we obtain analytical solutions for the equilibrium strategies and value function which depend on both current wealth and mortality intensity. Moreover, results for the constant risk aversion are presented as special cases of our models.

Keywords

time-consistent strategystochastic mortality intensity processmean–variance criterionHamilton–Jacobi–Bellman equation

MSC classification

Secondary: 93E20: Optimal stochastic control 91B30: Risk theory, insurance 91G10: Portfolio theory 91B70: Stochastic models
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 1 , July 2014 , pp. 66 - 90
Copyright
Copyright © 2014 Australian Mathematical Society 

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